Time-dependent linearized friction: a development on Lorentz’ energy argument
In 1918 the State Committee, chaired by professor Hendrik Antoon Lorentz, was commissioned to investigate the consequences of constructing the Dutch closure dam the Afsluitdijk. The Committee developed a process-based one-dimensional network model simulating separately the tidal and surge water levels. Essential was the energy argument applied to linearize the quadratic friction parametrization of the tidal model. Lorentz determined a steady friction coefficient by equaling the linearized energy dissipation to the quadratic. Recently, Reef (2016) continued the State Committee’s pioneering work by reconstructing their storm model and extending it to a non-stationary model which simulates the time-dependent forcing in the frequency domain. This study implements a time-dependent friction coefficient – based on Lorentz’ energy argument – in a linearized fashion which results in a convolution sum to the frictional term in the momentum equation. This couples each frequency in the spectrum, which is a large advantage since it enables interaction between frequencies (i.e. the interaction between tide and surge).